# solvable group

A group $G$ is solvable if it has a subnormal series

$$G={G}_{0}\supset {G}_{1}\supset \mathrm{\cdots}\supset {G}_{n}=\{1\}$$ |

where all the quotient groups^{} ${G}_{i}/{G}_{i+1}$ are abelian^{}.

Title | solvable group |
---|---|

Canonical name | SolvableGroup |

Date of creation | 2013-03-22 12:08:53 |

Last modified on | 2013-03-22 12:08:53 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 11 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 20A05 |

Synonym | solvable |

Synonym | soluble group |

Related topic | DerivedSubgroup |

Related topic | CompositionSeries2 |

Related topic | GaloisCriterionForSolvabilityOfAPolynomialByRadicals |